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Zur kepplimg eines exakten verfahrens mit einem heuristiscieb verfahren für die lösung ganzzahliger linearer optimierungsprobleme

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Optimization 1985年第3期16卷 391-400页

Combining an exact method with a heuristic approach possibilities for solving linear mixed integer optimization problems are investigated. For the considered exact method numerical results with problems from the practice are given. Proper heuristic methods are the interior path methods [2] for which numerical experiences are well-known or the so-called geometric approach [8], Deriving of sufficient conditions for the existence of feasible solutions is possible.

关键词： mixed-integer programming numerical solution interior path methods Primary:90 C 11 Secondary:65 K 05

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Multiobjective Optimization of Relief Well Operations to Improve Levee Safety

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JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING 2021年第7期147卷 04021041-04021041页

作者： Chen, Ye-Hong Tsai, Frank T-C Jafari, Navid H. Louisiana State Univ Dept Civil & Environm Engn 3255 Patrick F Taylor Hall Baton Rouge LA 70803 USA Louisiana State Univ Dept Civil & Environm Engn 3212D Patrick F Taylor Hall Baton Rouge LA 70803 USA

The factor of safety (FS) of levees and floodwalls with relief wells to underseepage is predicated on the blanket thickness and relief well performance. In urban environments with limited right of way, relief wells are an option for addressing underseepage and sand boil development. Instead of adding more wells if problems persist, this study investigates the potential of active pumping at relief wells as an alternative to increase levee and floodwall factor of safety against underseepage. Optimization of relief well operations is achieved by a multiobjective mixed-integer nonlinear programming (MOMINLP) approach. The relief well operations optimization is demonstrated at the Inner Harbor Navigation Canal (IHNC), New Orleans, Louisiana, near the Seabrook Bridge at Lake Pontchartrain. Relief well evaluation at the water level corresponding to the 500-year return storm shows high total head at most IHNC West relief well sites. Relief well operations optimization provides decision makers useful tradeoffs between averaged FS deficit, total pumping rate, and the number of pumping wells for making pumping decisions. This study found that the Pareto-optimal solutions provide reasonable pumping rates, where all of the midway between relief wells in the IHNC West may meet the requirement FS > 1.5. The study also found that minimizing the number of pumping wells and minimizing the total pumping rate are influential objectives for deriving efficient pumping strategies. Sensitivity analysis on IHNC water stage found that FS improvement becomes marginal after total pumping rate reaches a threshold, especially at low IHNC water stages. (C) 2021 American Society of Civil Engineers.

关键词： Relief wells Optimization Multiple objectives mixed-integer programming Inner Harbor Navigation Canal (IHNC)

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A progressive hedging-based matheuristic for the stochastic production routing problem with adaptive routing

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COMPUTERS & OPERATIONS RESEARCH 2024年 169卷

作者： Kermani, Ali Cordeau, Jean-Francois Jans, Raf HEC Montreal CIRRELT 3000 chemin Cote-Sainte-Catherine Montreal PQ H3T 2A7 Canada GERAD 3000 chemin Cote Sainte Catherine Montreal PQ H3T 2A7 Canada

The production routing problem (PRP) arises in the context where a manufacturing facility manages its production schedule, the delivery of goods to customers by a fleet of vehicles, and the inventory levels both at the plant and at the customers. The presence of uncertainty often complicates the planning process. In particular, production and distribution costs may significantly increase if demand uncertainty is ignored in the planning phase. Nevertheless, only a few studies have considered demand uncertainty in the PRP. In this article, we propose a two-stage stochastic programming approach for a one-to-many PRP with a single product and demand uncertainty. Unlike previous studies in the literature, we consider the case where routing decisions are made in the second stage after customer demands become known. This offers more flexibility, which can decrease transportation costs by preventing unnecessary customer visits. In addition to the static-dynamic case, in which setup decisions are made first and production quantities are decided in the second stage, we also consider the static-static setting where both sets of decisions must be made prior to the demand realization. A progressive hedging algorithm combined with a matheuristic is developed to solve the problem. The role of the progressive hedging algorithm is to decompose the stochastic problem into more tractable scenariospecific subproblems and lead the first-stage variables towards convergence by modifying their Lagrangean multipliers. However, solving the subproblems remains challenging since they include routing decisions, and we thus propose a matheuristic to exploit the structural characteristics of the subproblems. First, a Traveling Salesman Problem (TSP) is solved to find the optimal tour for all customers regardless of demand and capacity. Utilizing the sequence obtained from the TSP, we then solve a restricted PRP while taking into account the other constraints of the original problem. Finally, for

关键词： Production routing Stochastic programming Progressive hedging Matheuristic mixed-integer programming

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Risk-averse bi-level stochastic network interdiction model for cyber-security risk management

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INTERNATIONAL JOURNAL OF CRITICAL INFRASTRUCTURE PROTECTION 2021年 32卷 100408-100408页

作者： Bhuiyan, Tanveer Hossain Medal, Hugh R. Nandi, Apurba K. Halappanavar, Mahantesh Univ Tennessee Knoxville Dept Ind & Syst Engn Knoxville TN 37996 USA Mississippi State Univ Dept Ind & Syst Engn Mississippi State MS 39762 USA Pacific Northwest Natl Lab Richland WA 99352 USA

This paper proposes a methodology to enable a risk-averse, resource constrained cyber network defender to optimally deploy security countermeasures that protect against potential attackers with an uncertain budget. The proposed methodology is based on a risk-averse bi-level stochastic network interdiction model on an attack graph-maps the potential attack paths of a cyber network-that minimizes the weighted sum of the expected maximum loss over all attack scenarios and the risk of substantially large losses. The conditional-value-at-risk measure is incorporated into the stochastic programming model to reduce the risk of substantially large losses. An exact algorithm is developed to solve the model as well as several acceleration techniques to improve the computational efficiency. Numerical experiments demonstrate that the acceleration techniques enable the solution of relatively large problems within a reasonable amount of time: simultaneously applying all the acceleration techniques reduces the average computation time of the basic algorithm by 71% for 100-node graphs. Using metrics called mean-risk value of stochastic solution and value of risk-aversion, computational results suggest that the stochastic risk averse model provides substantially better network interdiction decision than the deterministic (ignores uncertainty) and risk-neutral models when 1) the distribution of attacker budget is heavy-right-tailed and 2) the defender is highly risk-averse. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Attack graph Stackelberg game mixed-integer programming Conditional-value-at-risk Cyber-security

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Co-optimization of thermal power plant flowchart, thermodynamic cycle parameters, and design parameters of components

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ENERGY 2020年第0期193卷 483-496页

作者： Kler, Aleksandr M. Potanina, Yulia M. Marinchenko, Andrey Y. Russian Acad Sci ESI SB RAS Siberian Branch Melentiev Energy Syst Inst 130 Lermontov Str Irkutsk Russia

The improvement in the efficiency of an energy plant depends on a rational development of its flowchart and choice of parameters along with the load schedule, equipment reliability, operating mode, etc. It is advisable to study such complex technical systems with the methods of mathematical modeling and optimization. The paper presents an approach to the development of optimal flowcharts and selection of parameters of energy plants. The approach is based on the combination of a method for optimization of the most complex flowchart and a method for solving discrete-continuous problems of nonlinear mathematical programming. A case study of the co-optimization of design parameters, operating parameters and equipment mix for the integrated gasification combined-cycle plant is demonstrated. The optimization calculations were carried out by the criterion of the minimum price of electricity for a given internal rate of return on investment and the maximum energy efficiency of the plant. Several optimal solutions meeting the different criteria are obtained. The proposed approach can be used for optimization of flowcharts and parameters of other complicated energy plants (high-efficiency combined-cycle plants, ultra-supercritical steam cycles, integrated power plants for electricity and synthetic liquid fuel co-production from coal, etc.). (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Mathematical modeling Thermal power plants Methods of optimization mixed-integer programming Reversible processes Branch-and-bound method

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Bi-criteria Pareto optimization to balance irradiation time and dosimetric objectives in proton arc therapy

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PHYSICS IN MEDICINE AND BIOLOGY 2022年第24期67卷 245017-245017页

作者： Wuyckens, Sophie Zhao, Lewei Saint-Guillain, Michael Janssens, Guillaume Sterpin, Edmond Souris, Kevin Ding, Xuanfeng Lee, John A. UCLouvain Mol Imaging Radiotherapy & Oncol MIRO Brussels Belgium Beaumont Hlth Dept Radiat Oncol Royal Oak MI USA UCLouvain ICTEAM Louvain La Neuve Belgium Ion Beam Applicat SA Louvain La Neuve Belgium KULeuven Dept Oncol Leuven Belgium

Objective. Proton arc therapy (PAT) is a new delivery technique that exploits the continuous rotation of the gantry to distribute the therapeutic dose over many angular windows instead of using a few static fields, as in conventional (intensity-modulated) proton therapy. Although coming along with many potential clinical and dosimetric benefits, PAT has also raised a new optimization challenge. In addition to the dosimetric goals, the beam delivery time (BDT) needs to be considered in the objective function. Considering this bi-objective formulation, the task of finding a good compromise with appropriate weighting factors can turn out to be cumbersome. Approach. We have computed Pareto-optimal plans for three disease sites: a brain, a lung, and a liver, following a method of iteratively choosing weight vectors to approximate the Pareto front with few points. mixed-integer programming (MIP) was selected to state the bi-criteria PAT problem and to find Pareto optimal points with a suited solver. Main results. The trade-offs between plan quality and beam irradiation time (static BDT) are investigated by inspecting three plans from the Pareto front. The latter are carefully picked to demonstrate significant differences in dose distribution and delivery time depending on their location on the frontier. The results were benchmarked against IMPT and SPArc plans showing the strength of degrees of freedom coming along with MIP optimization. Significance. This paper presents for the first time the application of bi-criteria optimization to the PAT problem, which eventually permits the planners to select the best treatment strategy according to the patient conditions and clinical resources available.

关键词： proton arc therapy multi-criteria optimization Pareto front mixed-integer programming scalarization bi-objective optimization

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Model predictive control for drift counteraction of stochastic constrained linear systems ?

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AUTOMATICA 2021年 123卷 109304-109304页

作者： Zidek, Robert A. E. Kolmanovsky, Ilya V. Bemporad, Alberto Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA IMT Inst Adv Studies Lucca Italy

The paper presents a stochastic MPC (SMPC) formulation suitable for maximizing the average time until a discrete-time linear system with additive random disturbance violates prescribed constraints. The SMPC procedure is based on a scenario tree that encodes the most likely system behavior for a given tree density, where each branch of the tree represents a specific evolution of the system that occurs with a certain probability. A mixed-integer linear program (MILP) is developed that maximizes the average time until constraint violation for a given scenario tree. Feedback is provided by reconstructing the scenario tree and recomputing the MILP solution over a receding time horizon based on the current state of the system. The average time until constraint violation achieved by the SMPC strategy approaches the optimal value as the scenario tree density is increased. Two numerical case studies, including an adaptive cruise control problem, demonstrate the effectiveness of the proposed SMPC strategy compared to dynamic programming solutions. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Stochastic control mixed-integer programming Model predictive control

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Instance-specific algorithm configuration via unsupervised deep graph clustering

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2023年第1期125卷

作者： Song, Wen Liu, Yi Cao, Zhiguang Wu, Yaoxin Li, Qiqiang Shandong Univ Inst Marine Sci & Technol Jinan Peoples R China Shandong Univ Sch Control Sci & Engn Jinan Peoples R China Singapore Management Univ Sch Comp & Informat Syst Singapore Singapore Eindhoven Univ Technol Fac Ind Engn & Innovat Sci Eindhoven Netherlands

Instance-specific Algorithm Configuration (AC) methods are effective in automatically generating high-quality algorithm parameters for heterogeneous NP-hard problems from multiple sources. However, existing works rely on manually designed features to describe training instances, which are simple numerical attributes and cannot fully capture structural differences. Targeting at mixed-integer programming (MIP) solvers, this paper proposes a novel instances-specific AC method based on end-to-end deep graph clustering. By representing an MIP instance as a bipartite graph, a random walk algorithm is designed to extract raw features with both numerical and structural information from the instance graph. Then an auto-encoder is designed to learn dense instance embeddings unsupervisedly, which facilitates clustering heterogeneous instances into homogeneous clusters for training instance-specific configurations. Experimental results on multiple benchmarks show that the proposed method can improve the solving efficiency of CPLEX on highly heterogeneous instances, and outperform existing instance specific AC methods.

关键词： Algorithm configuration Unsupervised graph embedding mixed-integer programming

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Optimal design and operation of River Basin Storage

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2020年 95卷 102061-102061页

作者： Burrow, Andy Newman, Alexandra Colorado Sch Mines Dept Mech Engn 1500 Illinois St Golden CO 80401 USA

The State of Colorado's Stream Simulation Model (StateMod) provides comparative analysis for historical and future water resource decisions and policies along the Lower South Platte River. In order to identify locations for increased water storage, our research uses simulated data produced by StateMod as input to a mixed integer-linear optimization model. This model minimizes the cost of meeting unmet demands by assigning network flow of, and designing additional storage for, excess water while adhering to constraints that force the physical and topographical structures of the river. Using historical, measured flow data from 1962 through 2012, we extend the capability of StateMod by considering solutions with the following characteristics: (1) a single-reservoir solution, (2) a solution in which we only expand existing reservoirs, and (3) a solution without the constraints in (1) or (2). We conclude that, for the time horizon considered, the optimal method to mitigate shortages is with the construction of a combination of smaller surface and sub-surface reservoirs, and a corresponding prescribed flow. The total increased storage volume is 25,378 acre-feet (AF). Our work can be used as a strategic analysis tool by planners and engineers to quickly identify the most effective reservoir locations and the order in which to build them, rather than examining every potential storage site and the time at which it should be built, if at all. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Water resource planning mixed-integer programming Underlying network structure Reservoir design River basin management

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Production scheduling under demand uncertainty in the presence of feedback: Model comparisons, insights, and paradoxes

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COMPUTERS & CHEMICAL ENGINEERING 2022年 168卷

作者： Avadiappan, Venkatachalam Gupta, Dhruv Maravelias, Christos T. Univ Wisconsin Madison Dept Chem & Biol Engn Madison WI USA Princeton Univ Dept Chem & Biol Engn Princeton NJ 08544 USA Princeton Univ Andlinger Ctr Energy & Environm Princeton NJ 08544 USA

We investigate the importance of accounting for uncertainty a priori in production scheduling in the presence of feedback. First, we examine different optimization models (deterministic, robust, and stochastic programming), used to generate the open-loop schedules and describe the modeling of uncertainty in each case. Second, we present a formal procedure for carrying out closed-loop simulations in order to study and compare the closed-loop performance across the models as attributes such as the demand uncertainty observation horizon, order size max-mean relative difference, and load on the process network are varied. Finally, we analyze the results of the simulations to draw insights on how the above attributes affect the closed-loop performance of the different models across networks and expound on the paradoxes observed.

关键词： Online scheduling Real-time optimization mixed-integer programming

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